I am new around here and subject of bayesian statistics. My question that is there any way to derive priori given posteriori estimation analytically?I googled and found some techniques like MAP, bayesian inference and congugate gradient descent.
2026-03-26 00:58:54.1774486734
Finding Priori Given Posteriori Estimation
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I doubt there is a good reason to want to do this but ...
The posterior probability or density is proportional to the product of the likelihood of the observation and the prior (with proportional interpreted as a multiplicative factor which makes the sum of the posterior probabilities or the integral of the posterior density be equal to $1$)
so the prior probability or density would be proportional to the likelihood of the observation divided by the posterior (though this division will not work when the likelihood and posterior are both $0$, as might happen with a Bayesian approach to the German Tank Problem)